Precessions and parameter constraints from quasiperiodic oscillations in a rotating charged black hole

TL;DR

This work investigates QPOs as probes of frame-dragging in a rotating regular magnetic black hole within nonminimal Einstein–Yang–Mills theory. It derives equatorial timelike geodesics and epicyclic frequencies, maps them to QPOs via the relativistic precession model (RPM), and constrains the BH parameters using MCMC against QPO data from five X-ray binaries. The analysis finds stringent upper bounds on the magnetic charge $|Q|/M$ and the nonminimal coupling $\lambda/M^4$, with best-fit masses and spins closely matching Kerr predictions, indicating GR’s strong-field validity. It also analyzes Lense–Thirring, geodetic, and general spin precession for stationary observers, revealing suppression of precession frequencies by the regular BH parameters and highlighting prospects for future high-precision timing missions to further test these models.

Abstract

We investigate quasi-periodic oscillations (QPOs) as a diagnostic tool for probing frame-dragging effects and accretion disk physics in the spacetime of a rotating regular magnetic black hole (BH). Specifically, we analyze the precession of bound orbits and the epicyclic oscillations of test particles under small perturbations in the equatorial plane. We demonstrate how the BH nonminimal coupling parameter (lambda/M^4) and dimensionless magnetic charge (Q/M) significantly influence the three fundamental epicyclic frequencies. By applying the relativistic precession model and employing Markov Chain Monte Carlo simulations (MCMC), we constrain the BH characteristic parameters, including mass, spin, magnetic charge, and nonminimal coupling, using observational QPO data from five X-ray binaries: GRO J1655-40, XTE J1859+226, H1743-322, XTE J1550-564, and GRS 1915+105. Furthermore, we examine the Lense-Thirring, geodetic, and general spin precession frequencies of a test gyroscope attached to a stationary observer around the black hole. Our theoretical results indicate that the regular charged black hole suppresses these precession frequencies compared with the Kerr black hole case.

Figures (12)

• Figure 1: The typical plot showing the dependence of the horizon radius on the rotation parameter $a$ and the magnetic charge $Q$, for selected coupling parameters. The solid curves are for the radius of the event horizon ($r_+$) while the dashed curves are for the Cauchy horizon ($r_-$), and their intersection describes the extremal case.
• Figure 2: The effective potential for the regular magnetic BH spacetime as a function of $r/M$ with specific values of $\mathit{\tilde{E}}$, and $\mathit{L}$. The vertical dashed lines indicate the position for each scenario for the minimal effective potential.
• Figure 3: The shape of the precession orbit for a test-particle around a rotating regular magnetic BH spacetime. The dotted black curves indicate the Kerr BH result.
• Figure 4: The trends of the radial (black curves), vertical (red curves), and orbital epicyclic (blue curves) frequencies as functions of the ratio $r/M$ are analyzed for various values of the spin, magnetic charge, and the nonminimal coupling parameters, respectively.
• Figure 5: The behavior of the periastron precession frequency $\nu_{per}$ is analyzed as a function of the ratio $r/M$ for fixed values of the magnetic charge $(Q = 0.5, 0.7)$. The spin parameter and the nonminimal coupling parameter are varied independently.